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Klein-Gordon equation in quantum field theory is known to suffer from the possibility of negative probability. So, the question is, despite this, Klein-Gordon describes spin-zero field. So, how can negative probability and scalar field co-exist?

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More on Klein-Gordon equation and negative probabilities in quantum mechanics: – Qmechanic Oct 14 '12 at 18:20
up vote 2 down vote accepted

In QFT, we reinterpret the probability density as the probability charge density. In other words, negative probabilities correspond to antiparticles.

In fact, the Dirac equation which describes spin-1/2 also has this property, and it led to the prediction of the positron as the antiparticle of the electron.

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but Wikipedia and say that negative probability density do not make sense, and this is the reason for developing Dirac equation... So.. what is that and this? – War Oct 14 '12 at 22:52
Yes, negative probabilities do not make sense. What physicists discovered was that they were not calculating the probability density, but ~ probability density * charge. So if charge is opposite, they get a negative answer, but the actual probability is positive definite. – hwlin Oct 15 '12 at 0:25

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